%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%% Kapitel 1:
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++


\chapter{Introduction}

Regression testing in software engineering has become one of the widely researched areas of engineering in recent times. Lot of extensive research has already been done in this area for past two decades. Regression testing is a frequently executed expensive process that is used to revalidate modified software. Regression testing ensures that the system is always taken into confidence for any potential side effects that might have been introduced after the changes were introduced. A collection of test cases is often stated as Test Suite. In an ideal test system, the best practices suggest running the entire test suite after every change. Unfortunately, certain factors such as cost, time and workforce hinder carrying out such an activity.

Model based regression testing has become one of the upcoming areas of research in recent times. One of reasons why this has garnered so much interest is because it involves testing of systems at a much higher level. Major benefits of using model based regression testing approaches include early testing, better complexity management and cost reduction in executing test cases.

Regression testing is broadly classified into two major strategies, namely retest-all strategy and regression test selection strategy. Due to the expensive nature of the retest-all strategy test selection is performed. RTS (Regression Test Selection) has garnered extensive interest in the research community to make regression testing more effective and reliable. Many authors have proposed various RTS techniques. These techniques have been designed to run only the subset of test cases. RTS techniques have been evaluated and reported to bring down the cost involved of retesting. RTS in software engineering is classified into two major areas, namely test case classification and test case prioritization.

\section{Motivation}

LMS signal received at mobile terminal contains severe fading in urban environment. LMS received signal is combination of three components direct signal, specular reflected wave and multipath components. The multipath components may consist of roadside trees, utility poles, hills and mountains, the ground, or a body of water. Typical multipath scenario is that in which received signal contains both the direct and reflected signal in the constructive or destructive manner.

\begin{description}

\item[Direct component] \hfill \\  Signal transmitted from the LMS satellite arives at mobile terminal in LOS condition without any blockage known as direct signal component. In non-LOS condition direct signal component is blocked by the tree or any other obstacles. Direct signal component is shown in figure ~\ref{fig:Propagation Characteristics of Satellite Communication Channel} by red color arrow.

\item[Specular reflected wave] \hfill \\ Specular reflected component is generally the reflected signal from the smooth surface like road, buildings, etc. If the amplitude of the specular reflected component is equal to the direct component with opposite phase then received signal face the severe fading. Figure ~\ref{fig:Propagation Characteristics of Satellite Communication Channel} shows specular reflected component by the road with blue arrow.

\item[Multipath Component] \hfill \\ The multipath component is a phase incoherent multi-path wave due to scattering on rough surfaces near the terminal that reect rays in all directions, or due to diffraction on building edges, etc \cite{M_2011}. Ideally direct or LOS signal is the main wanted signal. In general LMS mobile receiver will receive many signals resulting from the signal taking a large number of different paths. These paths may be the result of reflections from buildings, mountains or other reflective surfaces including water, etc. that may be adjacent to the main path. Multipath propogation shown in figure ~\ref{fig:Propagation Characteristics of Satellite Communication Channel} with black arrow.

\end{description}

Next section gives overview of two different statistical channel modelling approach.


\section{Statistical LMS Channel Model}


In general statistical modeling is mainly used to model LMS channel. There are many methods proposed for statistical channel modeling like two-state channel model, three-state channel model, etc.
 

\subsection{Three-State Statistical LMS channel model}

Three-state channel model proposed in \cite{threestate}, which describes a propagation channel in terms of three possible states (LOS, moderate shadow and deep shadow). The three state model was originally developed for low margin systems, where direct satellite to user terminal communication is only possible in LOS condition \cite{two-state}. 


Three-state LMS channel model works on existence of three different rate of change (fast, slow, very slow) in the received signal. If there is non-LOS condition such as mobile terminal goes in deep shadowed environment like behind the trees or buildings, it is described as very slow state.

This model uses Loo distribution to describe the signal variations within each state and first order Markov process to model state transitions between each state \cite{two-state}. 


The three states of propagation characteristics shown in Figure ~\ref{fig:State Information} with fast, slow and very slow variations.


\subsection{Two-State Statistical LMS channel model}

The other approach is two-state LMS channel model proposed in \cite{two-state}. For future LMS applications, non-LOS conditions demands more consideration. The accuracy of non-LOS modeling is achieved in two-state channel model, which is the revised model of the previous three state channel model.

For our work we will consider Two-State channel model because the non-LOS components are necessary and need to model more precisely under deep shadow conditions in Urban environments. Instead of three state in previous model, this model only consider two states to describe the propagation characteristics of LMS channel.

The two-state model considers only two states Good and Bad as shown in Figure ~\ref{fig:State Information}. These states are not required to match the LOS and non LOS conditions. Two-State channel model uses Loo distribution parameters to characterize the fading conditions within each states. As shown in Figure ~\ref{fig:State Information}, one entire set of Loo parameters are used to describe the two possible states. In this approach, first order Markov model or semi-Markov model is used to generate state transitions and state durations \cite{two-state}.



\begin{figure}[htb]
\centering
\includegraphics[width=\textwidth]{./bilder/states}
\caption{State Information according to propagation characteristics \cite{two-state}}
\label{fig:State Information}
\end{figure}

As we can see from Figure ~\ref{fig:State Information}, The Good state represents areas with unobstructed view of the satellite (less shadowed or unshadowed) represents high received signal power, whereas the Bad channel state represents areas where the direct satellite signal is shadowed by obstacles means low received signal power.

\section{Problem statement for Two-State channel model}

The focus of the report is to investigate state information of LMS received signal envelope required for modelling LMS channel using 'Two-State Statistical channel model' proposed in \cite{two-state}. Two-State Statistical channel model assumes two states of LMS channel Good state and Bad state. The states doesn't depend on LOS or non-LOS conditions (not necessarily matching LOS and Non-LOS conditions). Only one entire set of Loo distribution parameters are used to define the possible states.

For the accuracy of the channel simulators, it should need to change it's channel state as frequently as possible \cite{deterministic}. But for the channel simulator it will increase the computational complexity. The generation of new channel state is computationally expensive. For this reason the change of channel state should be made according to the measured signal change but not at higher rate.

A segmentation of LMS received signal into stationary region is required to do in advance. Only after the segmentation, small scale parameters are calculated correctly for that stationary segment \cite{filteri}. Measured data can not be used directly to calculate the small scale parameters of the channel.

For the accuracy of state oriented statistical channel model, it is necessary to accurately identify state change position based on stationarity region identification of channel.

Duration of states is dependent on the specific obstruction like house and buildings cause total blockage in the received signal, but obstacles like tree cause shadowed condition. Duration of blockage state is dependent on the obstacles size such as in urban environment poles or small buildings cause small blockage in the LOS condition. 

Previously proposed state identification methods: 

\begin{description}

\item [Global thresholding] \hfill \\ As proposed in \cite{BT_2002}, separation of Good and Bad state can be achieved by using the global fade depth threshold of -5 dB. In that approach local power level was used for separation of LOS condition from the shadowed or blockage condition. Three state statistical channel model was also using this approach with two fade depth threshold of -5 dB and -10 dB for separation of LOS, shadowed and blockage conditions.

\item [Clustering] \hfill \\ Use of clustering was another approach proposed in \cite{M_2011} for separation of LOS state from the shadowed or blockage state. K-means and Fuzzy C-means clustering were used for state identification. This method again use the global fade depth threshold for the clusters. As per the result of the report \cite{M_2011}, Fuzzy C-means provide better results compare to K-means clustering.

\end{description}


Identification of Good and Bad state according to received signal power levels using these approach can be possible.

Segmentation based on global thresholding on the received signal power level does not provide the accurate channel characteristics. Channel stationarity play an important role in the channel characteristics. LMS channel segmentation can be performed and based on that LMS channel state can be obtained.

In this report, we propose some LMS signal segmentation methodologies. Before starting to discuss the methodologies of LMS received signal segmentation, it is necessary to discuss the problems related to segmentation.


\section{Issues Related to Segmentation}

Received signal from Land Mobile Satellite (LMS) face several problems. Because of different types of obstacles such as high buildings, trees or tunnels, received RF power level signal suffers fading and influence the LOS condition. In urban scenario, it is necessary to identify that our mobile vehicle gone through partial or total outage in the satellite visibility, and the lack of integrity in the received pseudo-range measurement \cite{STCD_2008}.

At the mobile vehicle LMS signal can arrive as direct signal, specular reflected component and multipath signal or all at same time. LMS received signal contains the multipath signals in LOS condition or only multipath signal in non-LOS condition. In urban scenario, direct signal with multipath component is presents in the LOS condition. Because of the specular reflected component, density of the reflected obstacle is added to the direct RF component. Due to multipath effect received signal at mobile vehicle contains change in the variance with LOS mean level as shown in figure ~\ref{fig:LOS path with multipath components}.

\begin{figure}[htb]
\centering
\includegraphics[width=\textwidth]{./bilder/channel_condition_LOS}
\caption{LOS path with negligible multipath}
\label{fig:LOS path with negligible multipath}
\end{figure}

\begin{figure}[htb]
\centering
\includegraphics[width=\textwidth]{./bilder/channel_condition_NLOS}
\caption{Non-LOS path with specular reflected component and multipath component}
\label{fig:Non-LOS path with specular reflected component and multipath component}
\end{figure}

\begin{figure}[htb]
\centering
\includegraphics[width=\textwidth]{./bilder/channel_condition_LOS_multipath}
\caption{LOS path with multipath components}
\label{fig:LOS path with multipath components}
\end{figure}

In non-LOS situations where direct signal component is not present but only multipath and specular reflected components are present in the received RF signal . The specular reflected signal cause the mean change in the received RF signal level when direct signal component is not present as shown in figure ~\ref{fig:Non-LOS path with specular reflected component and multipath component}. Mean change in the received RF signal is caused by the specular reflected component if it's phase is opposite to the direct component and mean level is same as the direct signal.

The Two-state LMS channel model allows the Loo distribution corresponding to each of the two state to take different parameter triplet (Mean of direct signal, Standard deviation of direct signal and Multipath powers) $(M_A, \Sigma_A and MP)$ \cite{M_2011}. 

Initially detection of abrupt change problem was addressed using statistical approach. In this statistical approach change detection can be modelled with simple hypothesis testing, where only change and no change situations are present.

\begin{itemize}

\item $H0$: No change in the received signal
\item $H1$: Change in the received signal

\end{itemize}

This approach calculates the difference between distribution of the data set and provide the test statistics which is compared to threshold. Based on this test statistics change is detected.

To identify the state of LMS channel, segmentation of LMS received signal is required with the consideration of above mentioned triplet parameters. LMS channel components contains two dependent $M_A$ and $\Sigma_A$ and one independent parameters $MP$, so LMS channel segmentation requires more effort.

In the next part, state of the art for the change detection in three parameters are provided.


\section{State of the art}


LMS segmentation requires to detect changes in three parameters of the received signal. So segmentation of LMS signal problem comes into multiple hypothesis testing problem. 

In first case received signal is in LOS condition. In the second case, there is change in the mean means presence of the multipath components and specular reflected components. In the third case, there is no change in mean but only change in the variance of the received signal.

\begin{itemize}

\item $H0$: LMS mobile vehicle in LOS conditions. No change condition ~\ref{fig:LOS path with negligible multipath}.

\item $H1$: LMS mobile vehicle in LOS condition but with the presence of multipath component. Change in variance ($MP$) because of multipath component ~\ref{fig:LOS path with multipath components}.

\item $H2$: LMS mobile vehicle in non-LOS condition which contains multipath and specular reflected component. Change in mean ($M_A$) and variance ($MP$) because of specular reflected and multipath component ~\ref{fig:Non-LOS path with specular reflected component and multipath component}.

\end{itemize}


In the next part, standard deviation change detection can be applied as simple hypothesis testing separately on the direct signal.



This chapter presents the different channel modelling approaches. In the next section we discuss about the Motivation and Goal of the project. 




  
